► University of Kerala-MSc PHYSICS
UNIVERSITY OF KERALA
MSc Degree Programme (effective from 2001-02)
Branch II Physics
A. Course Structure & Mark Distribution
Semester | Paper Code | Paper | Contact hours per week | UE duration (h) | Maximum Marks | ||||
L | T | P | IA | UE | Total | ||||
I | PH 211 | Mathematical Methods in Physics | 6 | 1 | - | 3 | 25 | 75 | 100 |
PH 212 | Modern Optics & Electromagnetics | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 213 | Electronics | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 251 | General Physics | - | 1 | 4 | - | - | - | - | |
PH 252 | Electronics & Computer Science | - | 1 | 3 | - | - | - | - | |
Total for S1 | 18 | 5 | 7 | - | 75 | 225 | 300 | ||
II | PH 221 | Mechanics | 6 | 1 | - | 3 | 25 | 75 | 100 |
PH 222 | Quantum & Statistical Physics | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 223 | Computer Science | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 251 | General Physics | - | 1 | 3 | 6 | 25 | 75 | 100 | |
PH 252 | Electronics & Computer Science | - | 1 | 4 | 6 | 25 | 75 | 100 | |
Total for S2 | 18 | 5 | 7 | - | 125 | 375 | 500 | ||
III | PH 231 | Quantum Mechanics | 6 | 1 | - | 3 | 25 | 75 | 100 |
PH 232 | Atomic & Molecular Physics | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 233X | (Special Sub: Paper-I) | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 261 | Advanced Physics | - | 1 | 4 | - | - | - | - | |
PH 262 | (Special Subject) | - | 1 | 3 | - | - | - | - | |
Total for S3 | 18 | 5 | 7 | - | 75 | 225 | 300 | ||
IV | PH 241 | Condensed Matter Physics | 6 | 1 | - | 3 | 25 | 75 | 100 |
PH 242 | Subatomic Physics | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 243X | (Special Sub: Paper0II) | 6 | 1 | - | 3 | 25 | 75 | 100 | |
PH 261 | Advanced Physics | - | 1 | 3 | 6 | 25 | 75 | 100 | |
PH 262X | (Special Subject) | - | 1 | 4 | 6 | 25 | 75 | 100 | |
PH 201 | Project | - | - | - | - | - | 100 | 100 | |
PH 202 | Viva-voce | - | - | - | - | - | 100 | 100 | |
Total for S4 | 18 | 5 | 7 | - | 125 | 575 | 700 | ||
Grand Total | 72 | 20 | 28 | - | 400 | 1400 | 1800 | ||
X ..... E for Electronics; C for Computer Science | |||||||||
L: Lecture ...T: Tutorial ... P: Pratical .... IA: Internal Assessment ... UE: Univ. Exam |
B. General Guidelines
B-1 THEORY PAPERS
- In the syllabus, topics are distributed in different units to have an even distribution of topics. Hence, continuity is lost in certain cases Teachers are advised to rearrange such topics while teaching.
· Solutions of some typical problems in each topic shall be explained in the class. The students should be encouraged to solve more problems as assignments, which shall help them to face the State/National tests.
B-2 LAB COURSES
- The aim of each experiment shall be defined clearly.
- Error analysis should be done for each experiment and the final result, wherever possible, should be reported with estimated uncertainty.
- The design of electronic circuits is a part of experiment.
B-3 PROJECT WORK
- The aim of the project work is to bring out talents of students and to introduce research methodology to students.
- Project work may be chosen from any branch of physics, which may be experimental, theoretical, or computational.
- Emphasis should be given for originality of approach.
- The presentation style of the project report shall be in accordance with the format of a standard journal.
C. Pattern of Question Papers
C-1 THEORY
- Each question paper has three parts – Part A, Part B and Part C.
- Part A contains eight short answer questions spanning the entire syllabus. Of which the candidate has to answer any five questions.
- Part B contains three compulsory questions with internal choice. Each question shall be drawn form the same unit of the syllabus.
- Part C contains six problems spanning the entire syllabus. The candidate has to answer any three.
- The distribution of marks for the three parts is as follows:
Part | Question to be answered | Weight of each question | Total marks |
A | 5 out of 8 | 3 marks | 15 |
B | 3 (with internal choice) | 15 marks | 45 |
C | 3 | 5 marks | 15 |
Paper maximum ......... | 75 |
C-2 PRACTICALS
- PH 252 : Electronics and Computer Science has two units, viz., Unit A-Electronics (4 h duration with 50 marks) and Unit B-Computer Science (2 h duration with 25 marks).
- PH 261 : Advanced Physics has two parts, viz., Part A – Performance of one experiment with 50 marks and Part B – Analysis of a given data/spectrum with 25 marks.
Question paper pattern
MSc Degree Examination
Branch II Physics
PH2xy-------------------------------------
Duration: 3 hours Maximum marks: 75
Instructions to question paper setter
- Each question paper has three parts-Part A, Part B and Part C.
2. Part A contains eight short answer questions spanning the entire syllabus. Of which the candidate has to answer any five question carries three marks.
3. Part B contains three compulsory questions with internal choice. Each question shall be drawn from the same unit of the syllabus. Each question carries 15 marks.
4. Part C contains six problems spanning the entire syllabus. The candidate has to answer any three. Each question carries five marks.
Part A
(Answer any five question. Each question carries three marks.)
I a)
b)
c)
d)
e)
f)
g)
h ) (5x3=15 marks)
Part B
IIA (a)--------------------------------------------------------------------
(b)--------------------------------------------------------------------
(15 marks)
Or
IIB (a)----------------------------------------------------------------------
(b)----------------------------------------------------------------------
(15 marks)
IIIA (a) ------------------------------------------------------------------------
(b)-------------------------------------------------------------------------
(15 marks)
Or
IIIB (a)--------------------------------------------------------------------------
(b)---------------------------------------------------------------------------
(15 marks)
IVA (a)---------------------------------------------------------------------------
(b)--------------------------------------------------------------------------
(15 marks)
(Or)
IVB (a)------------------------------------------------------------------------------
(b)------------------------------------------------------------------------------
(15 marks)
PartC
(Answer any three question. Each question carries five marks.)
V(a)
(b)
(c)
(d)
(e)
(f) (3x5=15marks)
PH211 Mathematical Methods in Physics (6,1,0)
UNIT-I
q Complex variables(15h)
Functions of a complex variable-derivative and Cauchy-Reimann differential equations-line integrals of complex functions-Cauchy's integral formula-Taylor series-Laurent series-singular points of an analytic function- point at infinity-residues-Cauchy's residue theorem-evaluation of residues –evaluation of definite integrals by contour integration.
q Vector analysis,vector space, matrices(10h)
Vector algebra-gradient of scalar field-line integrals-surface and volume integrals-divergence and curl of a vector field-integral transforms.
Oorthogonal curvilinear coordinates-gradient,divergence, curl and Laplacian in cylindrical and spherical polar coordinates
Basis and dimension of space-sub space of a vector space-linear transformations-similarity transformations-eigen values and eigen vectors of matrices-digitalization of matrices-Cyley-Hamilation theorem.
q Delta and Green functions(6h)
Dirac delta function-properties-Green function in one dimension-linear oscillator –Green function in three dimensions-solution of Possion equations.
q Partial differential equations(5h)
Important differential equations in physics (statement only)-solution of partial differential equations by the method of seperation of variables(wave equation and Laplace's equation).
UNIT-II
q Special functions(20h)
Legendre differential equation- series solution-Legendre polynomial P_{n}(x)
recurrence relations-orthogonality of P _{n}(x)-expansion of plane wave in terms of Legendre polynomials-associated Legendre polynomials-orthogonal property of associated Legndre polynomial (statement only)-statement of Laguerre equation-Laguerre polynomial and associated Laguerre polynomials.
Bessel differential equation- series solution (statement only)-Bessel function of order 'n' of the second kind-recurrence formula for J_{n}(x)-expression for J_{n}(x) when 'n' is half an odd integer-orthogonality of J_{ n}(x)-integral representation of J_{n}(x)-special Bessel functions.
Hermite differential equation-series solution (statement only) hermite function H_{n}(x)-recurrence relations-generating functions for H _{n}(x)-orthogonality relation for H_{n}(x)-recurrence relations-generating functions for H_{n}(x)-orthogonality relation for H_{n}(x).
q Laplace transforms(7h)
Laplace transforms of elementary functions-inverse Laplace transforms-Laplace transform of derivatives-applications of Laplace transforms to simple differential equation.
q Fourier series and transforms(9).
Fourier series-Dirchlet conditions-Fourier series of even and odd functions-complex form of Fourier series-Fourier integral and its complex forms-Fourier transforms-inverse transform-Fourier sine and and cosine transforms-convolution theorem and Parseval identity-Fourier transform of derivstives-applications to the solution of wave equation in one demension.
UNIT III
q Tensor analysis(13h)
Transformations of co-ordinates in linear space-Einstein summation convention-contravarient and covariant tensors-symmetric and skew-symmetric tensors-addition, multiplication and contraction of tensors-metric tensor-tensor calculus-Christoffel symbols-covariant differentiation of tensors.
q Group theory(15h)
Definition of a group-elementary properties of a group-sub groups-cosets and classes-cyclic groups-homomorphism and isomorphism of groups—representation of groups-reducible and irreducible representations-orthogonality theorems-Lie groups-SU(2) and SU(3) groups and their representation.
q Probability(8h)
Laws of probability-discrete probability distributions-theory of combinations and permutations-Stirling approximation for the factorial-continuous distributions-moments and standard deviation Binomial distribution-Poisson distribution-normal distribution-distribution of a sum of normal variates-applications to experimental measurements.
Reference:
Churchill& Brown: Complex variables and applications, 5 ^{th} edn.(McGraw Hill)
Speigal: Vector analysis(Schaum series)
Bell : Special functions for scientists and engineers
Arfken & Weber : Mathematical methods for physicisls,4 ^{th} edn. (Academic press)
Joshi : Elements of group theory for physicists(Wiley Eastern)
Joshi : Matrices and tensors in physics(Wiley Eastern)
Tung : Group theory in physics (World Scientific)
Harper : Introduction to mathematical physics(PH1)
Rajaput : mathematical physics (Pragati)
Ghatak et al : Mathematical physics (Macmillan)
PH212 Modern Optics $ Electromagnetics (6,1,0)
UNIT-1
q Wave nature of light ( 15 h )
Vector wave equation – reflection and refraction at a plane boundary – Fresnel equation – two beam interferometry – multiple beam interference – Febry- Perot interferometer – multiplayer films – antireflection films – high reflectance films.
Fresnel – Kirchoff formula- Fraunhoffer and Fresnel d iffractions – applications of Fourier transform to diffraction.
q Holography and fibre optics(13 h)
Zone plate- contruction of a hologram- reconstruction-amplitude and phase hologram –applications of holography.
Propagation of light in a dielectric –propagation in planar dielectric wav guide – propagation in optical fibres- calculation of fibre bandwith – attenuation in optical fibres – fibre material and fabrication methods-connectors and couplers.
q Quantum and non-linear optics
Principle of lasers – laser rate equations-helium -neon laser-four level solid state laser- argon ion laser-dye laser- elementary ideas of non-linear optics-optical harmonic generation(principle)-phase matching conditions- ideas of parametric amplification –self focusing phenomena-optical phase conjugation and photo refractive materials (elementary ideas only).
UNIT-II
q Electrodnamics(14h).
Potential formulations of electrodynamics-scalar and vector potentials-gauge transformations-Coulomb gauge and Lawernence gauge-Lawerence force law in potential form.
Energy and momentum in electrodynamics-Newton's third law in electodynamics-Poyting theorem-Maxwell's strees.
q Electromagnetic waves(12h)
Em waves in nonconducting medium-plane wave in vaccum-energy and momentum of EM waves-propagation through linear media-reflection and transmission at normal and oblique incidence.
EM waves in conductors-modified wave equation-plane waves and conducting media reflection and transmission at a conducting surface.
q Transmission lines(8 h)
Transverse EM waves along a parallel plate transmission line-general transmission line equations-wave characteristics of finite transmission lines-transmission line impedance matching.
UNIT III
q Guided waves and wave guides(10 h)
Waves between parallel planes-TE,TM, TEM waves-rectangular wave guides-TE and TM waves.
q Electromagnetic radiation and antennas(18 h)
Dipole radiation-retarded potentials-electric dipole radiation-magnetic dipole radiation-radiation from arbirtrary distribution of charge and current.
Radiation from a point charge-Leinard-Wiechert potentials-fields of a point charge in motion-power radiated by point charge.
Antennas-radiation from a quarter wave monopole and half wave dipole-directivity-gain and effective aperture-array with sources.
q Relativistic electrodynamics(8 h)
Dipole radiation-retarded potentials- electric dipole radiation-magnetic dipole radiation-radiation from arbirtrary distribution of charge and current.
Radiation from a point charge-Leinard-Wiechert potentials-fields of a point charge in motion-power radiated by point charge.
Antennas-radiation from a quarter wave monopole and half wave dipole-directivity-gain and effective aperture-array with sources.
q Relativistic electrodynamics(8 h)
Magnetism as a relativistic phenomena-transformation of the field-electric field of a point charge moving uniformly-electromagnetic field tensor-electrodynamics in tensor notation-potential formulation of relativistic electrodynamics.
Reference:
Fowles: Introduction to modern optics(Holt Richart& Winston)
Mayor : Introduction to classical and modern optics(PH1)
Griffiths : Introductory electrodynamics(PH1)
Cheng : Field and wave electromagnetics(Wesley)
Jackson : Classical electorpdynamics (Wiley)
Ghatak & Thyagarajan : Optical electronics(Cambridge Univ.Press)
Ghatak&Thyagarajan : Lasers-theory applications (Macmillan)
Sibley : Optical communications (Macmillan)
Sharma : Fibre optics in telecommunications (TM11)
PH213 Electronics (6,1,0)
UNIT-1
q Power amplifiers(16 h)
Types of power amplifiers-series fed class A amplifier-series fed transformer coupled class B : push pull circuits-harmonic distortion in amplifiers-class C and D amplifiers-design considerations.
q Feedback in amplifiers (20 h)
Feedback principle-effect of feedback on stability-nonlinear distortion-input and output impedance-bandwidth-different types of feedback.
Criteria for oscillation-phase shift,Wein bridge, crystal oscillator-frequency stability-astable, monostableand distable multivibrators-Schmitt trigger-bootstrap-sweep circuits.
UNIT-II
q Operational amplifiers(16 h)
Differential amplifier-ideal and real op—amp-input and out put impedance-frequency response-applications : amplifiers, mathematical operations, active filters, waveform generators-analog computations-comparators-S and H circuit-voltage regulator.
q Optoelectronics(20 h)
Optical fibres: graded index step index fibres-refractive index profiles-propagation of optical beams in fibres-mode characteristics and cut off conditions-losses in fibrwes-signal distortion group delay-material and wave guide dispersion.
Optical sources: Light emitting diodes-LED structure-internal quantum efficienvcy-injection laser diode-comparison of LED and ILD.
Optical detectors : PN junction photo diodes-PN photo detectors-avalanche photo diode-performance comparison.
Optical amplifers : Need for OAS-principles and operations-performance comparison various OAs.
UNIT-III
q Digital electronics(20 h)
Minimization of functions using Karnagugh map-representations using logic gates-Flip-flops-RS, clicked RS, D and JK flip flops-counters: synchronous and asynchronous-shift registers-semiconductor memories: ROM, RAM,PROM,EPROM-decoders/demultplexers-encoders/multiplexers-multiplexing displays-A/D and D/A converters.
q Electronic measurement techniques(16 h)
Voltage and current sources-power supply-measurement of high and low resistance AC bridges and their applications-unbalance conditions-Wein bridge.
Ac voltmeter using rectifiers-RMS responding voltmeter-electornic multimeter-differential voltmeter-Q-meter.
Oscilloscopes-vertical deflection system-delay line-multiple trace-horizontal deflection system-oscilloscope techniques.
Function generator-signal generation-frequency counters-signal analyzer
Reference:
Milman&halkias : Integrated electronics (McGraw Hill)
Bolested: Electronic devices and circuit theory()
Ryder : Electronics-fundamentals and applications(PHI)
Cooper & Helfrick : Electronic instrumentation and measurement techniques(PHI)
Keiser : Optical fibre communications (McGraw Hill)
Agarwal : Nonlinear fibre optics(AP)
PH221 Mechanics(6,1,0)
UNIT-1
q Lagrangain formulaion (14 h)
Mechanics of a particle-mechanicas of a system of particles-D'Alembert principle and Lagrange equations-simple applications of Lagrangain formulation-generalized moments-cyclic coordinates-Ruth's procedure-symmetry properties and conversation laws-Noether's theorem.
Hamilton principle-derivation of Lagrange equations from Hamilton principle.
q Two body central force problem(12 h)
Reduction to one body problem-equations of motion-equivalent one dimensional problem-differential equation for the orbit in the case of integrable power law potentials-kepler problem-inverse square law force-scattering in central force field-Rutherford formula-Virial theorem.
q Small oscillations(10 h)
Small oscillations of dynamical systems-frequencies of free vibrations and normal coordinates-forced vibrations-oscillations with dissipation.
UNIT II
q Hamilton equations and canonical transformations(12 h)
Halmilton equations of motion-preservation of phase volume under Hamilton flow (Liouville theorem)-canonical transformations-generating functions-Poisson brackets-applications to simple problems.
q Hamilton-Jacobi equation(12 h)
Hamilton-Jacobi equation-harmonic oscillator problem as an example-separation of variables in the Hamilton-Jacobi equation-action-angle variable-Kepler problem.
q Motion of rigid bodies (12 h)
Independent coordinates of a rigid body-orthogonal transformations-Eulerian angles-Euler theorem on the motion of a rigid body-infinitesimal rotations-rate of change of a vector-Corioli force-force-free motion of symmetric top-Euler geometric equation motion of a heavy symmetric top.
UNIT-III
q Relativity (20 h)
Review of: postulates of special relativity-Lorentz trznsformations-addition of velocities-mass-energy relation.
Lorentz group-four vectors and tensors-relativistic particle dynamics-relativistic electrodynamics-relativistic Lagragain-covariant Lagrangain.
General theory of relativity-principle of equivalence-principle of general covariance-gravitational mass and inertial mass-curvature of space-time-energy transfer of matter(general ideas only).
q Introduction to nonlinear dynamics(8 h)
Nonlinear oscillations-pendulum equation and solution-elementary ideas of elliptic integrals and functions.
Phase plane analysis of dynamical systems-fixed-point analysis and stability-limit cycles.
q Chaos(8 h)
Chaos in dissipative systems-logistic map-period doubling-critical point and bifurcation-strange attractor-elementary ideas of fractals.
Wave motion-wave equation-phase velocity-group velocity-dispersion-nonlinearity-solitary wave solutions and solutions-optical solutions.
References:
Goldstein : Classical mechanics (Wiley/Narosa)
Rana& Jog : Classical mechanics(TMH)
Bhatia: Classical Mechanics (Narosa)
Pathria: Theory of relativity(Pergamon)
Bose : An introduction to the theory of relativity
Tabor : Chaos and integrability in nonlinear dynamics (Wiley)
Drazin & Johnson: Solitons-An introduction (CUP)
Biswas : Classical Mechanics (Allied)
Hilborn : Chaos and nonlinear dynamics (OUP)
PH222 Quantum and Statistical Physics (6,1,0)
UNIT-I
q Thermodynamics (5 h)
Laws of thermodynamics and their consequences-thermodynamic potentials-Maxwell relations-chemical potential-phase equilibria.
q Elements of classical statistics(7 h)
Phase space-microstates-concept of ensembles-chemical ensembles-Liouville's theorem-statistical equilibrium-Maxwel-Boltzman distribution-mean values- equipartition theorem.
q Statistical thermodynamics(12 h)
Entropy and probability-entropy and number of eign states-thermodynamic functions of monoatomic gas-partition function-translational partition function-partition function of atoms and diatomic molecules rotational partition function-ortho and para hydrogens-vibrational partition function.
q Phase transitions and chemical reactions(12 h)
Phase transition-conditions for phase equilibrium-first and second order phase transitions-critical indices-order parameter-London's theory-vander Waals fluid-Curie-Weiss molecular field theory.
Equilibrium constant of reactions-Saha's ionization formula.
UNIT-II
q Quantum mechanics-historical perspective(16 h)
Breakdown of classical physics-the old quantum theory-need for quantum mechanics-wave nature of paeticles-uncertainly principle-wave function-superposition principle-wave packet- time dependent Schrodinger equation-operators for energy and time-time independentSchrodinger equation-physical interpretation of the wave function-expection value of dynamical variables probability current density-Ehrenfest theorems-stationary states acceptability conditions for wave function.
q General formulation of quantum perspective(20 h)
Linear vector space-orthogonal vectors-linearly independent and dependent vectors expansion theorem-function space-linear operators eigen values and eigen vectors of operators-Hermition operators and their properties-Dirac bra and ket notation- basic postulates of quantum mechanics-general uncertainty relation-parity operator-momentum representation-operators for position and momentum in the momentum representation.
Matrix representation of operators and wave functions-equation of motion-time evolution of a system-Schrodinger, Heisenberg and interaction pictures harmonic oscillator in the matrix representation.
Space-time symmetries-space translation and conversation of linear momentum-time translation and conservation of energy-space rotation and conservation of angular momentum-space inversion and time reversal.
UNIT III
q Solution of Schrodinger equation of simple potentials(20 h)
Particle in an infinite square well-particle in a box-particle in a finite square well-square potential barrier and quantum mechanical tunneling-linear harmonic oscillator –free particle in one dimension-electron in a periodic potential-Bloch's theorem-Kronig-Penny model.
Two-particle system, general consideration-systems with special symmetry-rigid rotator-hydrogen atom-atomatic orbitals.
q Quantum statistics (16 h)
Indistingishability of similar particles-probability of eign states-Maxwell-Boltzman statistics Bose-Einstein statistics-Fermi-Dirac statistics-number of energy states in an energy range BE statistics applied to radiation-BE condensation-thermionic emission of electrons-spin Para magnetism of free electrons.
References:
Mathews & Venkatesan : A textbook of quantum mechanics(Tata MCGraw Hill)
Aruldhas : Molecular structure and spectroscopy(PHI)
Palmer &Rogalski : Advanced university physics (Gordon& Breach)
Agarwal&Prakash : Quantum mechanics (PHI)
Ghatak : introduction to quantum mechanics (Macmillan)
Gopal : Statistical mechanics and properties of matter
Glasston e : Theoretical chemistry(Van Nostrand)
PH223 Computer Science(6,1,0)
UNIT-I
q Microprocessors(36 h)
Introduction to ups : Internal architecture of 8085-instruction and data format-addressing modes-instruction set-introduction to assembly language programming-simple programs.
Interfacing memory and I/O devices: Adress space partitioning-memory interfacing –I/O interfacing-data transfer schemes-programmed data transfer-synchronous data transfer-asynchronous data transfer-interrupts-software and hardware polling-multiple interrupts- enabling, disabling and making tnterrupts-DMA data transfer.
Interfacing devices: Types of interfacing , devices –I/O ports-programmable peripheral interface-80255: features, programming, timing and applications-80259: features, programming, applications-programmable DMA controller –8251 USART.
UNIT –II
q Computer organization(18 h)
Basic concepts-functional organization-bus structures-addressing methods-information encoding-instruction formats-instruction sequencing-memory organization-memory hierarchy-cache memories-address mapping techniques.
Memory interlinking-virtual memories-input/output organization –data transfer-synchronization-interrupt handling-standard I/O channels-peripheral devices-hard disk-magnetic tapes-drums-CD ROMs-printers-VDU-computer networks-architecture-ISO reference model-topology design-connectivity analysis-backbone design.
q Operating systems(18 h)
Basic concepts and terminology-batch systems-time sharing systems-real time systems-uP systems-file systems-file concept-file operations-directory systems-file protection-allocation methods-implementation issues-memory management-resident monitors-swaping-fixed and variable partitions-paging segmentation-virtual memory concept-processor management-multprogramming concept-scheduling concept-scheduling algorithms-multiprocessor scheduling-concurrent process-device management-physical characteristics-FCFS scheduling-I/O scheduling –basic ideas DOS, Windows, Unix, Linux operating systems.
UNIT-III
q Programming with C++ (36 h)
C++ as super set of C-features common to C and C++-basic structure of C++ programmes-header files-main()-cin and cout functions-compilation and execution.
Data types- constants and variables-function variables and global variables-operators and expressions in C++.
Flow of control –conditional statements –iteration statements -switch statement conditional operators as alternative to IF- nested loops break statement- ext() function.
Structured data types – arrays – array initialization-storage classes –multidimensional arrays – matrix as two-dimensional array –elementary arithmetic operations-sorting of strings.
Functions-built in and user defined-defining a function-accessing as a function-passing arguments to functions-calling functions with arrays-scope rules for functions and variables.
Structures in C++-structure definition-entering data in structures.
Classes and objects-definition-class declaration-class function definitions-creating objects.
Pointers-use of pointers in place of arrays-pointer arrays of pointers.
File handling in C++-basic file operations serial and werquential files-file modes-reading and writing strings on to disks-cof() function.
Reference:
Hamacher, Vranesic & Zaky : Computer organization (McGraw Hill)
Mano: Computer architecture (Prentice Hall)
Tanenbaum &Woodhull : Operating systems0design and implementation (PHI)
Dietel : Operating system principles (Wesley)
Dewhurst & Stark : Programming in C++ (PHI)
Liberty &Koeogh: C++-an introduction to programming(PHI)
McGregor : Using C++ (PHI)
Ravichandran : Programming with C++(TMH)
PH231 Quantum Mechanics(6,1,0)
UNIT –I
q Angular momentum (15 h)
Angular momentum operators-computation relations-eigen values and eigen functions of and Lz-general angular momentum J-eigen values of J ^{2} and Jz-angular momentum matrices-spin angular momentum-Pauli spin matrices-spin functions of spin ^{1/2}systems-addition angular momentum-Clebsh-Gordon coefficients-computation of CG coefficients.
q Approximate methods for stationery problems(13 h)
Stationary perturbation theory for nodegenerate and degenerate levels-anharmonic oscillator with cubic and quartic perturbations-ground state of helium atom-Stark effecting the first excited state of hydrogen atom-Zeeman effect in hydrogen.
q Variation method(8 h)
Variation method for ground and excited state-application to ground state of hydrogen and helium atom.
UNIT-II
q WKB approximation(8 h)
WKB method-the connection formulas-barrier tunneling-application to alpha decay application to bound state-validity of WKB approximation.
q Time dependent perturbation theory(13 h)
Time dependent perturbation method-harmonic perturbation-transition probability-transition to continuum states-absorption and emission of radiation-dipole approximation-Einstrin coefficient-selection rule for harmonic oscillator and hydrogen atom-adiabatic and sudden approximation.
q Theory of scattering(15 h)
Scattering experiment-differential and total scattering crosssections- scattering amplitude partial wave analysis of scattering by central potential-phase shift-optical theorem convergence of partial wave series-scattering by rigidsphere-scattering by a square well Ramsaner-Townsend effect-resonance scattering.Scattering integral equation-Born approximation-application to scattering by square well, Yukwa and screened Coulomb potentials.
UNIT-III
q Systems of identical –particles(10 h)
Identical particles – construction of symmetric and anti symmetric wave functions – Slator determinant – Pauli exclusion principle- spin functions for two electrons-effect of spin in ground and first excited states of helium-central field approximation for many electron atoms-hartries self consistent fields-Hartree-Fork method –exchange terms and their significance.
q Relativistic wave equation(16 h)
Klein-Jordon equation for a free particle-plain wave solution-charge and current density-Dirac relativistic equation for free particle-Dirac matrices-position probability, density and particle-spin orbit interaction-magnetic moment of electron-spectrum of hydrogen atom-Lamp shift-Dirac equation in covariant form.
q Field theory(10 h)
Introduction-Lagrangain field theory-n0n-relativistic fields-relativistic fields-Klein-Gordon field-Dirac field-electromagnetic field.
References:
Mathews & Venkkatesan : A text book of quantum mechanics(TMH)
Bransden & Jochain : Introduction to quantum mechanics (ELBS)
Wagnare :Fundamentals of quantum mechanics(Wheeler)
Schiff : Quantum mechanics(MsGraw Hill)
Agarwal & Hariprakash : Quantum Mechanics (PHI)
Thankappan : Quantum Mechanics (Wiley)
Sakurai : Modern quantum mechanics (Wesley)
Sakurai : Advanced quantum mechanics(Wesley)
Merzbacher: Quantum mechanics (Wiley)
Ryder : Quantum field theory (CUP )
PH232 ATOMIC&Molecular Physics(6,1,0)
UNIT-I
q Atomic spectra(12 h)
Quantum states of an electron in atom-hydrogen atom spectrum-alkali spectra- Stern and Gerlach experiment-electron spin-spin orbit coupling-fine structure-two-electron systems-L-S and J-J coupling schemes- spectroscopic terms-Hund's rule-term reversal –normal and anomalous Zeeman effect-Paschen-Back effect-Stark effect for one electron atom-spin of the nucleus-hyperfine structure.
q Quantum theory of valence(10 h)
Coalent, ionic and vanderwals interaction-molecular orbital method-LCAO approximation-MO treatment of hydrogen molecule-bonding and antibonding orbitals-diatomic molecular orbitals-electronic configuration of molecules in the MO concept-VB method-Hilter-London theory of hydrogen molecule-hydrogen molecule in VB method-directed bonds-sp,sp ^{2},sp^{3 }hybridizations.
q Molecular symmetry (10 h)
Symmetry operations-symmetry elements-algebra of symmetry operations- multiplication table-matrix representations of symmetry operations-molecular point groups-reducible and irreducible representations-great orthogonality theorem-character table for C2V and C3v point groups(derivation not required)- symmetry species of point groups-infrared activity-Raman activity.
q Molecular spectroscopic methods (5 h)
Electromagnetic spectrum-types of molecular energies-spectroscopic methods: and over view width of spectral lines-absorption and emission of radiation-elements of dipole approximation and selection rules.
UNIT-II
q Rotation of molecules(12 h)
Classification of molecules –rotational selection rules-rotational spectra of rigid diatomic molecules-isotope effect in rotational spectra-intensity of rotational lines-non rigid rotator-linear polyatomic molecule-symmetric top molecules-effect of electric field on rotational spectra-rotational spectra with quadrupole interaction-microwave spectrometer –applications.
q Infrared spectroscopy(14 h)
Vibrational energy of diatomic molecules-IR selection rules-vibrational and rotation-vibration spectra of diatomic molecules-asymmetry of rotation-vibration band-vibrations of polyatomic molecules overtones and combination bands-Fermi resonance-hydrogen bonding-rotation-vibration spectra of linear polyatomic and symmetric top molecules-solid state effects in vibrational spectra-group frequencies-IR spectrophotometer-Fourier transform IR spectrophotometer-applications of IR spectroscopy.
q Raman scattering (10 h)
Classical and quantum theory of Raman scattering-rotational Raman spectra of linear and symmetric top molecules-vibrational Raman spectra-mutual exclusion principle-polarization of Raman lines-single crystal Raman spectra-Raman spectrometer-structure-determination using IR and Raman spectroscopy-Raman investifation of phase transition and proton conduction-resonance Raman scattering-surface enhanced Raman scattering-surface enhanced Raman scattering-applications.
UNIT-III
q Electronic spectra (12 h)
Vibrational coarse structure of electronic spectra-Deslander table-progressions and sequences-Franck-Condon principle-rotational fine structure of electronic spectra-dissociation-pre-dissociation specification of of electronic states of diatomic molecules-basic ideas of photoelectron spectroscopy of atoms and molecules.
q Nuclear magnetic resonance (10 h)
Principle-NMR instrumentation-relaxation process-Bloch equations-dipolar interaction-chemical shift-spin interaction-general features of proton high resolution spectra-NMR spectra of solids-magic angle spinning NMR-elementary ideas of magnetic resonance of nuclei- ^{13 }C, ^{19} F structure determination using NMR.
q Electron spin resonance (8 h)
Principle-ESR spectrometer-ESR hyperfine structure-ESR of free radicls in solution-ESR of quadrupole interaction-magnetic hyperfine interaction-applications.
References:
Aruldhas: Molecular structure and spectroscopy(PHI)
Straughan&Walker: Spectroscopy Vol.I,II,and III(Chapman & Hall)
Banwell: Fundamentals of molecular spectroscopy (TMH)
Herzberg: Molecular spectra and molecular structure,Vol I, II & III (VNR)
White: Introduction to atomic spectra (McGraw Hill)
PH241 Condensed Matter Physics(6,1,0)
UNIT-I
q Crystal structure (8 h)
Review of: crystal lattice-unit cell-symmetry elements-point groups-space group-Bravais lattices-typical crystal structures like NaCI,CsCI diamond and ZnS.
Diffraction of x-rays by crystals-Bragg condition-reciprocal lattice and diffraction-Ewald construction- Brillouin zones.
q Lattice vibrations (8 h)
Vibration of monoatomic and diatomic linear lattices-acoustical and optical phonons-phonon momentum-lattice specific heat in the Einstein and Debye models.
q Free electron theory (10 h)
Free electron Fermi gas-energy levels in one dimension-free electron gas in three dimensions-density of states-Fermil level-Pauli paramagnetism-heat capacity of electron gas-electrical and thermal conductivity of metals-Wiedmann-Franx law-temperature dependence of electrical resistivity.
q Band theory of solids (10 h)
Electrons in a periodic potential –Bloch theorem-Kroing- Penny model-origin of energy gap-effective mass-concept of hole-comparison of metals, semiconductors and insulators-evaluation of band structure-reduced zone scheme-tight binding approximation.
UNIT-II
q Semiconductors (16 h)
Semiconductors-intrinsic and extrinsic conduction-effective mass-Fermi level-electrical conductivity and other transport properties.
Excitons-semiconductor lasers- photoconductivity-quantum Hall effect.
q Magnetism (20 h)
Langevin diamagnetism equation-quantum theory of paramagnetism-Hund rules-adaiamagnetic demagetisation-paramagnetic suscepetibility of conduction electrons.
Ferromagnetic order-Curie point and exchange integral-neutron magnetic scattering-ferromagnetic order-susceptibility below Neel temperature-ferromagnetic domains-antiferromagnetic order-two sublattice model-super exchange interactions.
UNIT-III
q Excitations (16 h)
Excitations in solids-magnons-helicons= spin waves in electron gas-magnetic moments and spin-magnon interactions=Frohlich Hamiltonian –Kohn effect –polorons and mass enhancement-attractive interaction between electrons.
q Superconductivity(20 h)
Meissner effect-flux quantization-persistent current-phenomenological theory-London equation-Type I and type II superconductors- thermodynamics-Cooper pairs-BCS theory. Josephson effect –SQUIDS.
Reference:
Kittel: Introduction to solid state physics (wiley)
Dekker: Solid state physics(McMillan)
Azaroff: Introduction to solids(TMH)
Pillai: Problems and solutions in solid state physics(New Age)
Ramakrishnan&Rao: Superconductivity today(Wiley Eastern)
Kheer: principles of solid state physics (New Age)
Omar: Elementary solid state physics (Wesley)
PH242 Subatomic Physics (6,1,0)
UNIT-I
q Nuclear properties (12 h)
Nuclear radius-nuclear size from electron scattering experiments-nuclear mass and binding energy-angular momentum-parity and symmetry –statistics-magnetic dipole moment-measurement of magnetic moment of neutrons-electric quadrupole moment-nuclear disintegration processes-mirror nuclei-nuclear isomerism.
q Nuclear forces(12 h)
Characteristics of nuclear forces-ground state of deutron-magnetic moment of deutron-charge independence-spin dependence-noncentral forces-nucleon-nucleon scattering-scattering cross sections-low energy (n,p) scattering-partial wave analysis-singlets and triplet potentials-effective range theory-(p,p) scattering at low energies-high energy scattering-low energy (n,n) scattering-meson theory of nuclear forces.
q Nuclear models (12 h)
Liquid drop model-semi-emprical mass formula-mass parabola-stability against beta decay. Shell model-magic numbers-spin orbit coupling-predictions of shell model-angular momentum and parity of ground state-excited state-magnetic moments and Schmidt lines islands of isomerism.
Collective model-rotational and vibrational states.
Unified model-superconductivity model.
UNIT- II
q Radioactivity (13 h)
Theory of alpha decay-barrier penetration-theory of beta decay-Curi plots-comparative half-lives-allowed and forbidden transitions-selection rules-electron capture-parity violation-neutrino experimental determination of neutrino-measurement of nutrino helicity-gamma decay-multipole radiations-selection rules-internal conversion.
q Nuclear reactions(13 h)
Different types of nuclear reactions-conservation laws, equation-threshold energy-theories of nuclear reaction-elastic scattering and reaction crossections-partial wave analysis-compound nuclear reactions-unclear reactions in the resonance region-Breit-Wingner one level formula-optical model.
q Nuclear fission and fusion (10 h)
Mechanism of fission-Bohr-Wheeler theory –Neutrons released in the fission process-thermalization of neutrons-four factor formula-general aspects of reactor design-reactor types.
Nuclear fusion-thermonuclear reaction in stars-controlled thermo nuclear reactions.
UNIT-III
q Interaction of nuclear reaction with matter (7 h)
Stopping power and range-ionization and radiation losses-bremsstrahlung-photoelectric absorption –Compton scattering-pair production-biological effects of radiation.
q Nuclear instrumentation(9 h)
Lonixation chamber-proportional counter-GM counter-solid state detector-scinillation counter-bubble and cloud chambers-Cerenkov counter-spark chamber-semiconductor dectors.
q Particle physics(20 h)
Classification and properties of elementary particles-types of interactions between elementary particles-gravitational, electromagnetic, weak and strong interactions-elementary particle quantum numbers-lepton number-muon number-baryon number-isospin strangeness-charge parity-CPT theorm-conservation laws-elementary particle symmetry-unitary symmetry-SU(2) and SU(3) groups-eight fold way-Gellamn-Okuba mass formula-elementary ideas about quark model-concept of colored quarks-elementary ideas of gauge theory of strong and weak interaction.
Reference:
Enge: Introduction to nuclear physics(Addision Wesley)
Cohen: Concepts of nuclear physics(TMH)
Kenneth: Intoductory nuclear physics(Wiley)
Kaplan: Nuclear physics (Addision Wesley)
Evans: The automatic nucleus(McGraw Hill)
Tayal : Nuclear physics (Himalaya)
Roy & Nigam : Nuclear physics-theory and experiments (Wiley)
Marmier&Sheldon: physics of nuclei and particles (Academic)
David : Introduction to elementaru particles (Wiley)
Ryder : Elementary particles and symmetries (Gordon&Breach)
Segre : Nuclei and particles (Benjamin)
Gottified & Weisskopf: Concepts of particle physics(Oxford)
Burcham& Jobes: Nuclear and particle physics (Longman)
Ghoshal : Automatic and nuclear physics.
PH251 General Physics (0,1,4+3)
(At least 12 experiments to be performed)
1. Determination of Y and o-Cornu's method.
2. Velocity of sound in liquids using ultrasonics.
3. Analysis of absoption spectrum of liquids using spectrometer.
4. Frauhnhofer lines-identification of elements.
5. FP etalon-measurement of etalon thickness using spectrometer.
6. Michelson interferometer-determination of ٣,d ٣ and thickness of a mica film.
7. BH curve of iron using anchor ring-ballistic method.
8. Standardisation of a meter scale using helium-neon laser
9. Determination of e/k using a transistor.
10. Determination of 'h'-photoelectric effect.
11. Diffraction at single, double and multiple slits using He-Ne laser.
12. Anderason bridge(AC)-determination of inductance.
13. Diode valve-verification of Richardson equation.
14. Diode valve-Stefan law of radiation.
15. Speed of a vaccum pump.
16. Specific heat of graphite-variation with temperature.
17. Strain gauge-determination of Y of a metal bar.
18. determination of solar constant.
PH252 Electronics&Computer Science(0,1,3+4)
UNIT-I ELECTRONICS
(At least 10 experiments to be performed)
1. FET characteristics.
2. Single stage common emitter amplifier-frequency response.
3. Emitter follower and source follower.
4. Negative feedback RC amplifier.
5. Push pull amplifier-complementary pair.
6. UJT characteristics-relaxation oscillator.
7. RC phase shift oscillator .
8. Astable multivibrator-conversation to voltage controlled oscillator.
9. Multivibrator-monostable, bistable
10. Flip flops-RS,JK
11. Schmit trigger
12. Weinbridge oscillator
13. OPAMP circutes: inverting,non-inverting amplifier,voltage follower
14. OPAM applications: Summing, difference amplifier,scal changer
15. OPAMP integrator, differentiator
16. uP8085: complement of a number.
17. uP8085:addition and substraction-single and multiple bytes
18. realization of gates using IC7400 &IC7402.
19. Half address and full addres.
UNIT-II COMPUTER SCIENCE
A. Computer programming
( At least four programs to be done)
1. Least square fitting.
2. First derivative of a tabulated function by difference tables.
3. Numerical integration(Trapezoidal and Simpson methods)
4. Solution of algebraic and transcendental equations-Newton-Raphson method
5. Taylor series evaluation to find sin(x),cos(x),log(x), and exp(x)
6. Solution of first order differential equation- Runge –Kutta method.
7. Monte – Carlo method – determination of the value of π using random numbers
B. Applications in Physics
( At least six experiments to be performed )
1. Study of motion of a particle in a central force field
2. Study of scattering and absorption of a heavy ion by a nucleus
3. Verification of Kerpler laws
4. Simulation of wave function for a particle in a box
5. Scattering of a wave packet(potential hill and well)
6. Two – slit photon interference experiment
7. Simulation of Lennard Jones potential , binding parameters, elastic constant
8. Small oscillations of simple molecules – triatomic molecules for different bond constants
9. Simulation of ID-2D lattice vibrations
10. Simulation of random walk in one and higher dimensions
11. Computation of virial coefficients for a given potential.
PH261 Advanced Physics(0,1,4+3)
PART-A
(At least 10 experiments to be performed)
1. e/m of an electron-Thomson method
2. Charge of an electron -Millickan method.
3. Hydrogen spectra - determination of Rydberg constant
4. Absorption spectrum of iodine- determination of dissociation energy of I2
5. Study of the arc spectra of iron, copper ,Zinc and brass
6. Identification of elements by spectroscopic method
7. Structure determination of cubic crystals by XRD
8. Study of normal Zeeman effect
9. Hyperfine structure of spectral lines using FP etalon/LG plate
10. GM counter characteristics
11. Absorption of gamma rays by lead-mass absorption coefficient and half value thickness of the absorber.
12. AIO bands-photographing and analysis
13. Determination of Fermi energy.
14. Effect of carbon content variation on the tensile properites of steel.
15. Effect of ferromagnetic impurity in a weakly magnetic specimen-Guoy method.
16. magnetic susceptibility by Quincke method.
17. Determination of dielectric constant-lecher wire.
18. Determination of the band gap energy of semiconductors
19. Hall effect-determination of charge carrier density and carrier mobility in a doped semicondutctor.
20. Study of optical fiber characteristics.
PART - B
(Any five of the following experimental data/spectra to be analysed)
1. Analysis of the given band system.
2. Analysis of the given vibration-rotation spectrum
3. Interpretation of a Raman and IR spectra of simple of triatomic molecules
4. Dissociation energy of diatomic molecules- comparison of different spectroscopic methods
5. Analyses of XRD patterns
6. Identification of substances using XRD patterns using ASTM cards
7. Identification of elements from stellar spectra
8. Study of Doppler shifts of stellar spectra
9. Statistics of counting
PH233E Electronics-I(6,1,0)
UNIT I
· Amplitude modulation(12 h)
Amplitude modulation -AM transmitters and receivers - SSB balanced modulator -SSB generatio and reception.
· Angle modulation(12 h)
Frequency and phase modulation - equivalence between FM and PM - angle modulators and detectors -noise in FM.
· Digital comunication(12 h)
Elements of information theory- pulse transmission-PAM ,PTM,PCM codes- error detection and error codes - digital carrier systems .
UNIT-II
· Optical communication(18 h)
Introduction to optical communication systems -direct detection and hetrodyne receivers - advantages of coherent optical communications- optical digital communications - transmission link -introduction to solutions -soliton communicationsusing lumped amplifiers.
· Mobile cellular communication (18 h)
Basic cellular system-operation of cellular system-elements of cellular system design-frequency reuse-cochnnel interference reduction-desired C/N from a normal case in an omnidirectional antenna system-hand off mechanism-cell splitting-digital cellular systems-multiple access schems-global system for mobile-miscellaneous mobile systems.
UNIT-III
· Television(20 h)
TV systems and standards-B/W transmission-scanning-blanking and sychronizing pulses-B/W reception synchronizing circuits.
Basic principle of color TV-color theory-color TV systems: NTSC,PAL and SECAM(block schematic description)color TV picture tubes
· Radar (16 h)
Basic principles-radar equation-CW, pulse and MTI radar-Doppler radar-radar modulators-dyuplexer-radar displays.
Navigation-hyperbolic systems of navigation-LORAN,DECCA,DME and TACAN-landing systems.
Reference:
Roddy& Collen : Electronic Communications (PHI)
Kennedy : Electronic Communication Systems (McGraw Hill)
Keiser: Optical fibre communications (McGraw Hill)
Agarwal:Nonlinear fibre optics(AP)
Gagliarddi&Karp: Optical communications (Wiley)
Lee: Mobile cellular telecommunications (McGraw Hill)
Gulati: Monochrome and color television (Wiley Eastern)
Dhake: Television and video engineering(TMH)
Skolnik: Intoduction to radar systems(TMH)
Nagaraja: Elements of electronic navigation(TMH)
PH 243E Electronics –II (6,1,0)
UNIT –I
- Advanced uPs (36 h)
Intel 8086: architecture – addressing modes – accessing immediate and register date – accessing memory – accessing I/O ports – relative addressing mode – implied addressing mode – instruction set – instruction format – assembler dependent instructions – system design using 8086 – basic system concepts – interfacing memory 0 programmed I/O – 8086 based microcomputer – basic ideas about 8088, 80186, 80286, 80385,80486 and Pentium processors – coprocessor – Intel 8087 – RISC processors.
UNIT –II
- Artificial intelligence (36 h)
Introduction – problem solving methods – problem graphs – matching – heuristic functions – measure of performance and analysis of search algorithm.
Knowledge representation: representation using predicate logic – resolution in prepositional and predicate logic – uniform algorithm – structure representation of knowledge.
Planning: natural language understanding – perception learning – introduction to AI languages.
Expert systems: type of expert systems – their components and architecture. Knowledge acquisition – knowledge representation – production base system – frame based system.
Inference: backward chaining – forward chaining – rule value approach – fuzzy reasoning – certainty factors – construction of an expert system – language and tools – typical expert system examples.
UNIT –III
- Digital signal processing (36 h)
Introduction – continuous and discrete signals – ADC/DAC/discrete signals and systems – frequency analysis – continuous time signals – discrete time signal – Fourier transform and properties – applications – digital filters – power spectrum estimation – estimation of auto correlation – adaptive signal processing.
Comparison of digital and analog signal processing – multi channel and multi dimensional signals – sampling theorem – quantization and amplitude adaptive filters – neural net work – fractals and signal processing.
References:
Gaonkar: Microprocessor architecture – programming and applications with 8085/8080A (Wiley)
Brey: The Intel microprocessors – 8086/8088,80186,80286,80386,80486 (PHI)
Intel: Intel architecture software developers manual Vol. 2: Instruction set and reference & Vol.3: System Programming guide.
Rich: Artificial intelligence (McGraw Hill)
Cawsey: The essence of artificial intelligence (PHE)
Patterson: Introduction to artificial intelligence and expert systems (PHI)
Parkis & Manolkis: Digital signal processing (PHI)
Roman: Introduction to digital signal processing (McGraw Hill)
Schafer: Digital signal processing (PHI)
Streams & Davis: Signal processing algorithms (PHI)
PH262E Electronics (0,1,3+4)
UNIT –I
(At least seven experiments to be performed)
- Differential amplifier
- Crystal oscillator
- Amplitude modulation and demodulation
- Pulse code modulation and demodulation
- Opamp – active filters
- Opamp – waveform generation (astable, monostable, multivibrator, triangular)
- IC555 applications
- Voltage regulator (IC741) & three terminal adjustable VR
- BCD to decimal and BCD tp 7 segment decoder
- Decoder/Driver/Seven segment display
- Shift counter
- Ring counter
- A/D converter
- D/A converter
- Sequence generator
UNIT –II
(At least five experiments to be performed)
- Waveform generation using 8085
- Waveform generation using 8255
- Binary to ASCII and ASCII to BCD
- Interfacing ADC, DAC, stepper motor to 8085/8051 kit
- Interfacing: LED moving graphic display board
- Temperature controller
- Measurement of voltage and current using uP
- 8086: Assembly language programming
- IEEE 488: electrical interfacing
Posted by our guest writer S . If there is any content violations Report the Administrator by clicking "Report Problem".
0 comments :
Post a Comment
Comment.. and check "Notify me" for following comments to your email.
If you are experiencing any difficulty in posting comments, then try another browser. (example use Google Chrome)